Clarke is one of three main candidates in the frame, along with Aberdeen’s Derek McInnes and Scotland Under-21 head coach Scot Gemmill.

The Scottish FA (SFA) is closing in on making an appointment following Alex McLeish’s sacking last month.

“It’s a pinnacle of anyone’s career,” said Dyer.

“If the country comes for him it would be a great honour. I know he knows that.

“He has done a great job here. He’s always left it open that he will decide at the end of the season, that’s no secret. At the end of the day, it is a hard one to turn down.

“We will just leave it up to the gaffer. What will be, will be.”

Kilmarnock and Aberdeen have been kept informed as the SFA conducted due diligence on their respective bosses.

The SFA wants to make an appointment quickly, with the squad for the Euro 2020 qualifiers against Cyprus and Belgium scheduled to be announced in less than a fortnight.

Clarke arrived at Rugby Park in 2017 on a three-year deal, taking over from Lee McCulloch with the club joint bottom of the Scottish Premiership.

Kilmarnock host Rangers on Sunday (15:00 BST) and if they match or better Aberdeen’s result against Hibernian, which kicks off at the same time, they will clinch European football and a third-placed finish.

“I think it would be [a wrench for Clarke to leave],” added Dyer. “He’s been there for two years. He’s had two great seasons. The club has come on big strides.

“We have been blessed to have a good squad. The boys are good professionals and work hard every day. We know what he has achieved here is unbelievable to be fair, with the budget that he has.”